Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.Abstract:
It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.read more
Citations
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Journal ArticleDOI
Surface tension and contact angle of a liquid–solid interface
TL;DR: In this paper, the van der Waals model was used to calculate the variation in contact angle with liquid species for a given solid at fixed temperature, and the authors compared the results with the results of a liquid film and a solid substrate.
Book ChapterDOI
The Role of Pressure Solution Creep in the Ductility of the Earth’s Upper Crust
TL;DR: A review of the role of pressure solution creep in the ductility of the Earth's upper crust and how this creep mechanism competes and interacts with other deformation mechanisms is presented in this article.
Journal ArticleDOI
Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
Charles M. Elliott,Stig Larsson +1 more
TL;DR: In this article, a finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidiscrete case and in a completely discrete case based on the backward Euler method.
Journal ArticleDOI
The Cahn-Hilliard Equation with Logarithmic Potentials
TL;DR: In this paper, the authors discuss recent issues related with the Cahn-Hilliard equation in phase separation with the thermodynamically relevant logarithmic potentials; in particular, they are interested in the wellposedness and the study of the asymptotic behavior of the solutions (and more precisely the existence of finite-dimensional attractors).
Journal ArticleDOI
Surface induced self assembly in thin polymer films
TL;DR: The effect of boundary surfaces on phase separation and micro-phase separation in binary polymer blends and block copolymers has gained increasing attention over the last 5 years as mentioned in this paper, and the possibility to actively control the domain morphologies via surface interactions in view of possible technological applications.
References
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Journal ArticleDOI
The Principle of Corresponding States
TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Book ChapterDOI
Zur Theorie des Austauschproblems und der Remanenzerscheinung der Ferromagnetika
TL;DR: The Slatersche Methode as mentioned in this paper is an analog zur Jordan-Kleinschen Theorie in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als Spindichte gedeutet werden kann.
Journal ArticleDOI
Die Keimbildung bei der Ausscheidung in metallischen Mischkristallen
TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Journal ArticleDOI
Domain Structure of Rochelle Salt and K H 2 P O 4
Toshito Mitsui,Jiro Furuichi +1 more
TL;DR: In this paper, it has been shown that rochelle salt in the ferroelectric state consists of many domains and that the domain structure in an annealed crystal is caused by the electrostatic self energy.